What is the Free Space pocket in the bag for? I assume it's so you can pick out items from any pocket to keep them together, but how would that work in battle?

You can store any item in the bag in the Free Space for fast n' easy convenience. I usually store things that I rapidly use like Super Repels and TM 26. In battle, however, it's still sorted the way it would be as if the Free Space didn't exist. So you could have all your potions under Free Space, but in battle it would be under "Medicine."

Here is what I have learned (So my own knowledge):

The Free space it to organize things that you want to in one area rather than having to look though many large bags just to find what you are looking for. An example for what you might use it for would be if you are going to a cave and you think you need certain items with you, you might take Escape Rope, A potion or two, etc. So to find what you want more easily, you can just move those items up there. This isn't used in-battle, because when you use and item it is organized and filtered for you.

Did this help?

I dont believe so. If it matters, I think it is arranged in alphabetical order when you put things in there.

What I use the free space for is items that I'm looking to sell. Whether it's to the Pokémart or waiting for a collector. This way I don't accidentally sell something that I might want to keep. I thought it was a pretty innovative idea though, because you can use it for whatever you'd like!

*makes note to devote entire free space to competitive items and Power items in the future*

Something tells me this will be a spectacular help in organization of items you don't want to lose.

Not to mention that while in the Free Space pouch you can use the magnifying glass icon to sort the items so you only see what they would be in specific bags. Like only regular items, only medicine, only TMs, etc.

At least they offer more than the default (by type) sorting method now. Alphabetical can be nice in late game.

By the end of the game, you'll probably have all the highest healing medicines in there, the most damaging TMs, and frequently used held items. Plus your Repel of choice (Super Repel for me.) Also, even though I haven't tested this out in a while because I'm rich, I think if you completely use up an item that was in the Free Space and go buy some more, it will go back to the Free Space automatically. Of course, I'm not entirely sure, so you might want to test that out.
Edit: Yeah, it'll automatically go back to the Free Space. I bought some Lemonades, threw 'em in the convenience pouch, used 'em all up, bought a few more, and they automatically went to the Free Space. I just LOVE BW2, the little changes and things that happen just make it all the more better!